Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}x+2y &= 4 \\ 7x-2y &= -2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = -7x-2$ Divide both sides by $-2$ to isolate $y$ $y = {\dfrac{7}{2}x + 1}$ Substitute this expression for $y$ in the first equation. $x+2({\dfrac{7}{2}x + 1}) = 4$ $x + 7x + 2 = 4$ Simplify by combining terms, then solve for $x$ $8x + 2 = 4$ $8x = 2$ $x = \dfrac{1}{4}$ Substitute $\dfrac{1}{4}$ for $x$ back into the top equation. $ \dfrac{1}{4}+2y = 4$ $\dfrac{1}{4}+2y = 4$ $2y = \dfrac{15}{4}$ The solution is $\enspace x = \dfrac{1}{4}, \enspace y = \dfrac{15}{8}$.